Downward Path Preserving State Space Abstractions
Bibliographic record
Abstract
Abstraction is a popular technique for speeding up planning and search. A problem that often arises in using abstraction is the generation of abstract states, called spurious states, from which the goal state is reachable in the abstract space but for which there is no corresponding state in the original space from which the goal state can be reached. The experiments in this paper demonstrate that this problem may arise even when standard abstraction methods are applied to benchmark planning problem domains: spurious states cause the pattern databases representing the heuristics to be excessively large and slow down planning and search by reducing the heuristic values. Known automated techniques to get rid of a large portion of spurious states turn out to avoid the memory problem, while at the same time not avoiding the problem of bad heuristic quality. The main contribution of this paper is theoretical. We formally define a characteristic property—the downward path preserving property (DPP)—that guarantees an abstraction will not contain spurious states. How this property can be achieved is studied both for techniques focussing on automated domain-independent abstraction and for techniques focussing on domain-specific abstraction. We analyze the computational complexity of (i) testing the downward path preserving property for a given state space and abstraction and of (ii) determining whether this property is achievable at all for a given state space. Strong hardness results show a close connection between these decision problems and the plan existence problem in typical planning settings including sas and propositional strips. On the positive side, we identify formal conditions under which finding downward path preserving abstractions is provably tractable and show that some popular heuristic search and planning domains have an encoding that matches these conditions. This includes a new encoding of the Blocks World domain, for which DPP abstractions can be easily defined.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.002 | 0.011 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.002 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.002 | 0.003 |
| Open science | 0.002 | 0.004 |
| Research integrity | 0.001 | 0.003 |
| Insufficient payload (model declined to judge) | 0.004 | 0.001 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".